Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
public class Funky {
public static int ptr(int a){
return	a*(a+1)/2;
}
public static void main(String [] args){
Scanner in=new Scanner(System.in);
int n=in.nextInt();
int a=46000;
int b=1;
boolean flag=false;
//System.out.println(a);
while(ptr(b)<=ptr(a)){
int cnt=ptr(a)+ptr(b);
//System.out.println(cnt);
if(cnt==n){
flag=true;
break;
}
else if(cnt<n)
b++;
else if(cnt>n)
a--;
}
if(flag)
System.out.print("YES");
else
System.out.print("NO");
}
}